A uniform cube of side a mass m rests on a rough horizontal table as shown. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3 a / 4 above the base. The minimum value of F for which the cube begins to tip about an edge is (α m g/β). Find (aβ) (assume that cube does not slide).

Question

A uniform cube of side a mass m rests on a rough horizontal table as shown. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3 a / 4 above the base. The minimum value of F for which the cube begins to tip about an edge is (α m g/β). Find (aβ) (assume that cube does not slide). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For topling about edge x x prime F min . (3 a/4)=m g (a/2) F min .=(2 m g/3) .

For topling about edge xx′ Fmin.​43a​=mg2a​ Fmin.​=32mg​.

For topling about edge $x x^{'}$
$F_{m i n .} \frac{3 a}{4} = m g \frac{a}{2}$
$F_{m i n .} = \frac{2 m g}{3} .$